Shokei Shoujo no Virgin Road: Soshite, Kanojo wa Yomigaeru

The Lost Ones are wanderers who come here from a distant world known as "Japan." No one knows how or why they leave their homes. The only thing that is certain is that they bring disaster and calamity. The duty of exterminating them without remorse falls to Menou, a young Executioner. When she meets Akari, it seems like just another job...until she discovers it's impossible to kill this girl! And when Menou begins to search for a way to defeat this immortality, Akari is more than happy to tag along! So begins a journey that will change Menou forever...

(Source: Yen Press)